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Glite Dictionary
algebraic number

algebraic number

9.5
A number that solves a polynomial equation with rational coefficients
  • noun
  • /ˌæl.dʒəˈbreɪ.ɪk ˈnʌm.bər/
  • Specialized
translation icon : número algebraico
  • Mathematicians study algebraic numbers to understand the properties of solutions to polynomial equations.

Examples

  • For example, the square root of 2 is an algebraic number because it is a root of the polynomial x^2 - 2.

  • Is zero an algebraic number?

  • Every integer is an algebraic number because it is a root of a simple polynomial equation.

  • The square root of 2 is an algebraic number, as it satisfies the equation x² - 2 = 0.

  • Unlike π, which is transcendental, the cube root of 8 is an algebraic number.

  • An algebraic number can be expressed as a solution to a polynomial equation.

  • An algebraic number is defined as a solution to a polynomial equation, such as x^2 - 2 = 0.

Surface Forms

algebraic number singular
algebraic numbers plural

Morphology

algebraic + number

The compound directly combines 'algebraic' (related to algebra) and 'number', so a B1 learner who knows both words would likely infer it refers to a number used in algebra. However, the precise technical definition (a root of a polynomial with rational coefficients) is specialized and not predictable from the constituents alone, so the expression gives a general idea but not the formal meaning.

Etymology

Algebraic number comes from algebraic, the part of math where you solve equations, and number, the value you find; for example, solving x^2 - 2 = 0 gives sqrt(2), the value that makes the equation true. So algebraic number means 'a number that is a solution of an algebra equation'.